The non–linear polarizabilities of the hydrogen atom have been thoroughly studied throughout the years [1]}, [2]}, providing a good starting point for the study of these same non–linear processes in excitons. Recently, the non–linear optical effects from intra–excitonic transitions have been the focus of many theoretical and experimental works. This has been performed for several TMDs, including but not limited to \(\mathrm {WSe}_{2}\)  [3]}, [4]} and \(\mathrm {WS}_{2}\)  [5]}, [6]}, as well as \(\mathrm {hBN}\)  homostructures [7]}. Through doping processes, the optical non–linear properties of TMDs can be tuned [8]} which, along with their large non–linear optical coefficients [9]}, increases their feasibility for practical aplications [10]} (e.g., as optical modulators).
